Mixed Operations Math Word Problems 2 Worksheet for 3rd - 5th ... - Free Printable

Let’s solve each problem one by one, step by step.

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Problem 1:

Your brother traveled 117 miles in 2.25 hours. What is the average speed?

Average speed = total distance ÷ total time

So:
117 ÷ 2.25

To make it easier, multiply numerator and denominator by 100 to eliminate decimals:

11700 ÷ 225

Now divide:

225 × 50 = 11,250 → too big
225 × 52 = 225×50 + 225×2 = 11,250 + 450 = 11,700 → perfect!

So, 117 ÷ 2.25 = 52

✔ Average speed = 52 miles per hour

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Problem 2:

You have 15 yards of ribbon for 20 gift boxes. Each box gets the same amount. How much ribbon per box?

Total ribbon = 15 yards
Number of boxes = 20

Ribbon per box = 15 ÷ 20 = 3/4 yard

(You can think: 15 ÷ 5 = 3, 20 ÷ 5 = 4 → so 3/4)

✔ Each box gets 3/4 yard of ribbon.

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Problem 3:

Sam gave Jen 1/2 of his jujubes.
Jen ate 1/2 of what she got → so she kept 1/2 of that half.
Then she gave Kyle the rest (which is also 1/2 of her half).
Kyle ate 1/8 of what he got, and gave the last 10 to Kim.

We need to find how many jujubes Jen ate.

Let’s work backwards from Kyle giving 10 to Kim.

Kyle had some amount. He ate 1/8 of it, so he gave away 7/8 of it — and that equals 10.

So:
7/8 of Kyle’s jujubes = 10
→ Kyle’s total = 10 ÷ (7/8) = 10 × (8/7) = 80/7 ≈ 11.428... Wait — that’s not a whole number. That can’t be right.

Wait — let me re-read:

“Kyle ate 1/8 of the jujubes and gave the last 10 to Kim.”

That means: after eating 1/8, he gave the remaining 7/8 to Kim? But it says “gave the last 10 to Kim” — implying that after eating 1/8, the rest was 10.

So if he ate 1/8, then 7/8 = 10 → same as above → 80/7 — still not integer.

But maybe I misread. Let me read again:

> Sam gave Jen 1/2 of his jujubes. Jen ate 1/2 of the jujubes and gave the rest to Kyle. Kyle ate 1/8 of the jujubes and gave the last 10 to Kim.

Ah! Important: When it says “Jen ate 1/2 of the jujubes” — does that mean 1/2 of ALL jujubes, or 1/2 of what she got?

Looking at context: “Sam gave Jen 1/2 of his jujubes. Jen ate 1/2 of the jujubes...”

It probably means 1/2 of what she received — otherwise it would say “of Sam’s jujubes”.

Same with Kyle: “ate 1/8 of the jujubes” — likely meaning 1/8 of what he received.

Let’s assume that.

Let S = total jujubes Sam had.

Sam gave Jen: (1/2)S

Jen ate 1/2 of what she got → so she ate (1/2)*(1/2)S = (1/4)S

She gave the rest to Kyle → which is also (1/2)*(1/2)S = (1/4)S

Kyle got (1/4)S

He ate 1/8 of what he got → so he ate (1/8)*(1/4)S = (1/32)S

He gave the rest to Kim → which is (7/8)*(1/4)S = (7/32)S

And that equals 10.

So:

(7/32)S = 10
→ S = 10 * (32/7) = 320/7 ≈ 45.714 — still not integer.

Hmm. Maybe “the jujubes” refers to the original total?

Try this interpretation:

Let T = total jujubes Sam started with.

Sam gave Jen: (1/2)T

Jen ate 1/2 of THE JUJUBES → meaning 1/2 of T? That would be weird because she only got half.

But let’s try:

If Jen ate 1/2 of T, but she only received 1/2 T — that would mean she ate all she got, and gave nothing to Kyle — contradiction.

Alternative interpretation — perhaps “the jujubes” in each case refers to what they currently have.

Let’s define:

Let J = number of jujubes Jen received = (1/2) * Sam’s total

Jen ate 1/2 of J → so she ate (1/2)J

Gave the other (1/2)J to Kyle

Kyle received K = (1/2)J

Kyle ate 1/8 of K → so he ate (1/8)K

Gave the rest to Kim: (7/8)K = 10

So:

(7/8)K = 10 → K = 10 * 8 / 7 = 80/7 — again not integer.

This is problematic. Maybe there's a typo or I'm missing something.

Wait — perhaps “Kyle ate 1/8 of the jujubes” means 1/8 of the original total? Unlikely.

Another idea: maybe “gave the last 10 to Kim” means that after eating 1/8, the remainder was 10 — so 7/8 of what Kyle had = 10 → Kyle had 80/7 — not possible.

Unless we accept fractions? But jujubes are discrete.

Perhaps the problem meant: Kyle ate 1/8 of what he had, and gave the remaining 10 to Kim — so yes, 7/8 = 10 → Kyle had 80/7 — impossible.

Wait — let me check online or think differently.

Actually, let’s suppose that when it says “Kyle ate 1/8 of the jujubes”, it means 1/8 of what Jen gave him — and “gave the last 10” means the rest after eating is 10.

So if Kyle received X, ate (1/8)X, gave (7/8)X = 10 → X = 80/7 — still bad.

Unless the 10 includes something else? No.

Perhaps “the last 10” means he gave 10, which is the remainder after eating 1/8 — so yes.

Maybe the problem has a mistake, or I need to interpret "the jujubes" as the current holding.

Let’s try working backwards with integers.

Suppose Kyle gave 10 to Kim, and that was 7/8 of what he had (since he ate 1/8).

So what he had before eating: let’s call it C.

C - (1/8)C = 10 → (7/8)C = 10 → C = 80/7 — not integer.

But 80/7 is approximately 11.428 — not possible.

Unless he ate 1/8 of the original total? Let’s try that.

Let T = total jujubes.

Sam gave Jen: T/2

Jen ate 1/2 of T? But she only has T/2 — so she can't eat more than she has.

If she ate 1/2 of what she has, that's T/4, gave T/4 to Kyle.

Kyle has T/4.

If Kyle ate 1/8 of T, then he ate T/8, but he only has T/4, so T/8 ≤ T/4 — ok.

Then he gave the rest to Kim: T/4 - T/8 = T/8 = 10

So T/8 = 10 → T = 80

Then Jen ate T/4 = 80/4 = 20

Let’s verify:

Sam had 80.

Gave Jen 40.

Jen ate 1/2 of the jujubes — if "the jujubes" means the original total, then she ate 40? But she only has 40 — so she ate all, gave nothing to Kyle — contradiction.

If "the jujubes" for Jen means what she received, then she ate 20, gave 20 to Kyle.

Kyle has 20.

If he ate 1/8 of the original total, that's 10, so he ate 10, gave 10 to Kim — matches!

And "gave the last 10 to Kim" — yes.

So interpretation: when it says "ate 1/8 of the jujubes", it means 1/8 of the original total that Sam had.

Similarly for Jen: "ate 1/2 of the jujubes" — might mean 1/2 of original, but she only has half, so if she ate 1/2 of original, that's 40, but she only has 40, so she ate all, gave nothing — doesn't work.

In this case, for Jen, if she ate 1/2 of what she received, that's 20, gave 20 to Kyle.

For Kyle, if he ate 1/8 of original total (80), that's 10, and he had 20, so he gave 10 to Kim — works.

But the phrase is "Kyle ate 1/8 of the jujubes" — if "the jujubes" refers to the original batch, then yes.

Perhaps it's ambiguous, but this gives integer answers.

So let's go with that.

Total jujubes T = 80

Sam gave Jen: 40

Jen ate 1/2 of what she got: 20 (so she ate 20)

Gave 20 to Kyle

Kyle ate 1/8 of original total: 80/8 = 10

Gave remaining 10 to Kim — perfect.

So Jen ate 20.

✔ Answer: 20

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Problem 4:

You save $2 in January, $4 in February, $8 in March, $16 in April, and this pattern continues through December.

Pattern: each month you double the previous month’s savings.

January: 2 = 2^1

February: 4 = 2^2

March: 8 = 2^3

April: 16 = 2^4

...

December is the 12th month, so 2^12

Sum from n=1 to 12 of 2^n

This is a geometric series.

Sum = 2 + 4 + 8 + ... + 2^12

First term a = 2, ratio r = 2, number of terms n = 12

Sum = a*(r^n - 1)/(r - 1) = 2*(2^12 - 1)/(2-1) = 2*(4096 - 1) = 2*4095 = 8190

Check: 2^1 = 2, 2^2=4, ..., 2^12=4096

Sum = 2+4+8+16+32+64+128+256+512+1024+2048+4096

Add step by step:

2+4=6

6+8=14

14+16=30

30+32=62

62+64=126

126+128=254

254+256=510

510+512=1022

1022+1024=2046

2046+2048=4094

4094+4096=8190

Yes.

✔ Total saved: $8190

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Problem 5:

It takes 6 cubes to build a staircase with 3 steps.

How many cubes for 11 steps?

Look at the diagram: for 3 steps, it shows:

Bottom row: 3 cubes

Middle row: 2 cubes

Top row: 1 cube

Total: 3+2+1 = 6 — matches.

So for n steps, it’s sum from 1 to n: n(n+1)/2

For 3 steps: 3*4/2 = 6 — correct.

For 11 steps: 11*12/2 = 66

✔ Answer: 66 cubes

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Problem 6:

Jon has 1/2 pizza left.

At breakfast, he ate 1/3 of that.

What fraction of the original pizza did he have left for lunch?

He had 1/2 originally left.

Ate 1/3 of that: so he ate (1/3)*(1/2) = 1/6 of original pizza.

So left: 1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3

Alternatively: he had 1/2, ate 1/3 of it, so 2/3 of the leftover remains.

2/3 of 1/2 = (2/3)*(1/2) = 2/6 = 1/3

✔ Fraction left for lunch: 1/3

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Final Answers:

1. 52 mph
2. 3/4 yard
3. 20
4. $8190
5. 66
6. 1/3

──────────────────────────────────────

Final Answer:
1. 52
2. \frac{3}{4}
3. 20
4. 8190
5. 66
6. \frac{1}{3}